With your poor magnetic circuit - the iron core only halves the length of air that your H-field has to push flux through - you are going to need all the Ampere.Turns you can get, as it only doubles the field compared to an air core.
To get maximum strength from the magnet, you need to (a) wind as much copper on there as possible and (b) dissipate as much power in it as it will allow. This is independent of voltage, current, turns or wire gauge - they are related as we shall see, but only the mass of copper and the power dissipated actually affect the magnetic field independently.
The maximum power you can use is governed by the maximum temperature it can reach, and the magnet duty cycle. If you want to operate it continuously, then you are limited by its cooling. If you want to apply a single pulse, then you are limited by its heat capacity. Needless to say, most realistic use cases fall between these two simple extremes. It's safest to design for the continuous case. If you can plan for, let's say, a 10% duty cycle, then you can use three times more current than the continuous limit. However, if you operate at 30% or 100% for too long, it will overheat. It's quite easy to operate at 100% if your software crashes - you may want to implement a watchdog to shut the magnet supply down if the software fails.
Once you have decided what power you can use, you change the turns and wire gauge to match your power supply. More turns of thinner wire - higher voltage lower current. Fewer turns of thick wire - lower voltage higher current. But in each case, it's the same total power.
A series resistor will simply increase the voltage needed at the power supply for any given magnet current, so avoid it in the final design. It can be a useful way of limiting the current while you are experimenting though.